from typing import (
    Any,
    Literal as L,
    NoReturn,
    SupportsIndex,
    SupportsInt,
    TypeAlias,
    TypeVar,
    overload,
)

import numpy as np
from numpy import (
    complex128,
    complexfloating,
    float64,
    floating,
    int32,
    int64,
    object_,
    poly1d,
    signedinteger,
    unsignedinteger,
)
from numpy._typing import (
    ArrayLike,
    NDArray,
    _ArrayLikeBool_co,
    _ArrayLikeComplex_co,
    _ArrayLikeFloat_co,
    _ArrayLikeInt_co,
    _ArrayLikeObject_co,
    _ArrayLikeUInt_co,
)

_T = TypeVar("_T")

_2Tup: TypeAlias = tuple[_T, _T]
_5Tup: TypeAlias = tuple[
    _T,
    NDArray[float64],
    NDArray[int32],
    NDArray[float64],
    NDArray[float64],
]

__all__ = [
    "poly",
    "roots",
    "polyint",
    "polyder",
    "polyadd",
    "polysub",
    "polymul",
    "polydiv",
    "polyval",
    "poly1d",
    "polyfit",
]

def poly(seq_of_zeros: ArrayLike) -> NDArray[floating]: ...

# Returns either a float or complex array depending on the input values.
# See `np.linalg.eigvals`.
def roots(p: ArrayLike) -> NDArray[complexfloating] | NDArray[floating]: ...

@overload
def polyint(
    p: poly1d,
    m: SupportsInt | SupportsIndex = ...,
    k: _ArrayLikeComplex_co | _ArrayLikeObject_co | None = ...,
) -> poly1d: ...
@overload
def polyint(
    p: _ArrayLikeFloat_co,
    m: SupportsInt | SupportsIndex = ...,
    k: _ArrayLikeFloat_co | None = ...,
) -> NDArray[floating]: ...
@overload
def polyint(
    p: _ArrayLikeComplex_co,
    m: SupportsInt | SupportsIndex = ...,
    k: _ArrayLikeComplex_co | None = ...,
) -> NDArray[complexfloating]: ...
@overload
def polyint(
    p: _ArrayLikeObject_co,
    m: SupportsInt | SupportsIndex = ...,
    k: _ArrayLikeObject_co | None = ...,
) -> NDArray[object_]: ...

@overload
def polyder(
    p: poly1d,
    m: SupportsInt | SupportsIndex = ...,
) -> poly1d: ...
@overload
def polyder(
    p: _ArrayLikeFloat_co,
    m: SupportsInt | SupportsIndex = ...,
) -> NDArray[floating]: ...
@overload
def polyder(
    p: _ArrayLikeComplex_co,
    m: SupportsInt | SupportsIndex = ...,
) -> NDArray[complexfloating]: ...
@overload
def polyder(
    p: _ArrayLikeObject_co,
    m: SupportsInt | SupportsIndex = ...,
) -> NDArray[object_]: ...

@overload
def polyfit(
    x: _ArrayLikeFloat_co,
    y: _ArrayLikeFloat_co,
    deg: SupportsIndex | SupportsInt,
    rcond: float | None = ...,
    full: L[False] = ...,
    w: _ArrayLikeFloat_co | None = ...,
    cov: L[False] = ...,
) -> NDArray[float64]: ...
@overload
def polyfit(
    x: _ArrayLikeComplex_co,
    y: _ArrayLikeComplex_co,
    deg: SupportsIndex | SupportsInt,
    rcond: float | None = ...,
    full: L[False] = ...,
    w: _ArrayLikeFloat_co | None = ...,
    cov: L[False] = ...,
) -> NDArray[complex128]: ...
@overload
def polyfit(
    x: _ArrayLikeFloat_co,
    y: _ArrayLikeFloat_co,
    deg: SupportsIndex | SupportsInt,
    rcond: float | None = ...,
    full: L[False] = ...,
    w: _ArrayLikeFloat_co | None = ...,
    cov: L[True, "unscaled"] = ...,
) -> _2Tup[NDArray[float64]]: ...
@overload
def polyfit(
    x: _ArrayLikeComplex_co,
    y: _ArrayLikeComplex_co,
    deg: SupportsIndex | SupportsInt,
    rcond: float | None = ...,
    full: L[False] = ...,
    w: _ArrayLikeFloat_co | None = ...,
    cov: L[True, "unscaled"] = ...,
) -> _2Tup[NDArray[complex128]]: ...
@overload
def polyfit(
    x: _ArrayLikeFloat_co,
    y: _ArrayLikeFloat_co,
    deg: SupportsIndex | SupportsInt,
    rcond: float | None,
    full: L[True],
    w: _ArrayLikeFloat_co | None = ...,
    cov: bool | L["unscaled"] = ...,
) -> _5Tup[NDArray[float64]]: ...
@overload
def polyfit(
    x: _ArrayLikeFloat_co,
    y: _ArrayLikeFloat_co,
    deg: SupportsIndex | SupportsInt,
    rcond: float | None = ...,
    *,
    full: L[True],
    w: _ArrayLikeFloat_co | None = ...,
    cov: bool | L["unscaled"] = ...,
) -> _5Tup[NDArray[float64]]: ...
@overload
def polyfit(
    x: _ArrayLikeComplex_co,
    y: _ArrayLikeComplex_co,
    deg: SupportsIndex | SupportsInt,
    rcond: float | None,
    full: L[True],
    w: _ArrayLikeFloat_co | None = ...,
    cov: bool | L["unscaled"] = ...,
) -> _5Tup[NDArray[complex128]]: ...
@overload
def polyfit(
    x: _ArrayLikeComplex_co,
    y: _ArrayLikeComplex_co,
    deg: SupportsIndex | SupportsInt,
    rcond: float | None = ...,
    *,
    full: L[True],
    w: _ArrayLikeFloat_co | None = ...,
    cov: bool | L["unscaled"] = ...,
) -> _5Tup[NDArray[complex128]]: ...

@overload
def polyval(
    p: _ArrayLikeBool_co,
    x: _ArrayLikeBool_co,
) -> NDArray[int64]: ...
@overload
def polyval(
    p: _ArrayLikeUInt_co,
    x: _ArrayLikeUInt_co,
) -> NDArray[unsignedinteger]: ...
@overload
def polyval(
    p: _ArrayLikeInt_co,
    x: _ArrayLikeInt_co,
) -> NDArray[signedinteger]: ...
@overload
def polyval(
    p: _ArrayLikeFloat_co,
    x: _ArrayLikeFloat_co,
) -> NDArray[floating]: ...
@overload
def polyval(
    p: _ArrayLikeComplex_co,
    x: _ArrayLikeComplex_co,
) -> NDArray[complexfloating]: ...
@overload
def polyval(
    p: _ArrayLikeObject_co,
    x: _ArrayLikeObject_co,
) -> NDArray[object_]: ...

@overload
def polyadd(
    a1: poly1d,
    a2: _ArrayLikeComplex_co | _ArrayLikeObject_co,
) -> poly1d: ...
@overload
def polyadd(
    a1: _ArrayLikeComplex_co | _ArrayLikeObject_co,
    a2: poly1d,
) -> poly1d: ...
@overload
def polyadd(
    a1: _ArrayLikeBool_co,
    a2: _ArrayLikeBool_co,
) -> NDArray[np.bool]: ...
@overload
def polyadd(
    a1: _ArrayLikeUInt_co,
    a2: _ArrayLikeUInt_co,
) -> NDArray[unsignedinteger]: ...
@overload
def polyadd(
    a1: _ArrayLikeInt_co,
    a2: _ArrayLikeInt_co,
) -> NDArray[signedinteger]: ...
@overload
def polyadd(
    a1: _ArrayLikeFloat_co,
    a2: _ArrayLikeFloat_co,
) -> NDArray[floating]: ...
@overload
def polyadd(
    a1: _ArrayLikeComplex_co,
    a2: _ArrayLikeComplex_co,
) -> NDArray[complexfloating]: ...
@overload
def polyadd(
    a1: _ArrayLikeObject_co,
    a2: _ArrayLikeObject_co,
) -> NDArray[object_]: ...

@overload
def polysub(
    a1: poly1d,
    a2: _ArrayLikeComplex_co | _ArrayLikeObject_co,
) -> poly1d: ...
@overload
def polysub(
    a1: _ArrayLikeComplex_co | _ArrayLikeObject_co,
    a2: poly1d,
) -> poly1d: ...
@overload
def polysub(
    a1: _ArrayLikeBool_co,
    a2: _ArrayLikeBool_co,
) -> NoReturn: ...
@overload
def polysub(
    a1: _ArrayLikeUInt_co,
    a2: _ArrayLikeUInt_co,
) -> NDArray[unsignedinteger]: ...
@overload
def polysub(
    a1: _ArrayLikeInt_co,
    a2: _ArrayLikeInt_co,
) -> NDArray[signedinteger]: ...
@overload
def polysub(
    a1: _ArrayLikeFloat_co,
    a2: _ArrayLikeFloat_co,
) -> NDArray[floating]: ...
@overload
def polysub(
    a1: _ArrayLikeComplex_co,
    a2: _ArrayLikeComplex_co,
) -> NDArray[complexfloating]: ...
@overload
def polysub(
    a1: _ArrayLikeObject_co,
    a2: _ArrayLikeObject_co,
) -> NDArray[object_]: ...

# NOTE: Not an alias, but they do have the same signature (that we can reuse)
polymul = polyadd

@overload
def polydiv(
    u: poly1d,
    v: _ArrayLikeComplex_co | _ArrayLikeObject_co,
) -> _2Tup[poly1d]: ...
@overload
def polydiv(
    u: _ArrayLikeComplex_co | _ArrayLikeObject_co,
    v: poly1d,
) -> _2Tup[poly1d]: ...
@overload
def polydiv(
    u: _ArrayLikeFloat_co,
    v: _ArrayLikeFloat_co,
) -> _2Tup[NDArray[floating]]: ...
@overload
def polydiv(
    u: _ArrayLikeComplex_co,
    v: _ArrayLikeComplex_co,
) -> _2Tup[NDArray[complexfloating]]: ...
@overload
def polydiv(
    u: _ArrayLikeObject_co,
    v: _ArrayLikeObject_co,
) -> _2Tup[NDArray[Any]]: ...
